Well, the problem with this scenario is that the whole Austrian empire was held together by dynastic bonds and royal prerogatives. If those go away, there’s nothing keeping it together.
That said, though, if the scenario is an 1848-like revolution starting in Austria and spreading to the rest of the Holy Roman Empire (sans Prussia), and the new Austrian leader is proclaimed “President of Germany” or “Imperial Consul” or something of that nature, that’s a whole different ballgame. Are we assuming here that this Revolutionary Austria has a Napoleon-like figure who can hold the state together against enemies on all sides?